MathDB

d | \overline{aabbcc} iff d | \overline{abc} where d is two digit number

Source: Czech-Polish-Slovak Junior Match 2013, Individual p4 CPSJ

March 14, 2020

dividesdivisornumber theoryDigits

Problem Statement

Determine the largest two-digit number

d

with the following property: for any six-digit number

\overline{aabbcc}

number

d

is a divisor of the number

\overline{aabbcc}

if and only if the number

d

is a divisor of the corresponding three-digit number

\overline{abc}

.
Note The numbers

a \ne 0, b

and

c

need not be different.